"We assured him we're going to keep to our schedule," Baucus said, adding that he still plans on a Finance Committee markup this month and a bill on the Senate floor in July.

While the senators conceded that they discussed "three or four" sticking points on the legislation, they declined to go into detail.

Only Enzi said he communicated to the president some concerns he and other Republicans have.

"I'm a little worried about the timeline, and I'm a little worried about how we pay for it," Enzi said, adding that the administration has already "maxed out the credit card."

Grassley emphasized that the president is pushing for a bipartisan bill, and he said his idea of a proposal endorsed by both sides of the aisle "is not a Democratic bill with five or six Republicans going along with it."

But Grassley noted that Obama is not giving in on his push to get a bill soon.

"I thought the president was flexible except in one area, and that was 'get something done,' " Grassley said.

Grassley Tweeted over the weekend that the president had "nerve" by pushing for the deadline: "Pres Obama you got nerve while u sightseeing in Paris to tell us 'time to deliver' on health care. We still on skedul/even workinWKEND.

"When you are a 'hammer' u think evrything is NAIL I’m no NAIL," Grassley wrote in another Twitter post.